It seems that lot of students are confused about the confidence intervals 
and how they relate to Welch's procedure.

1) Confidence Intervals are meant to be created from any N sample points
representing any statistic. E.g. points X1, X2,...Xn could represent
heights of a sample of n students in IIT. Then instead of stating
just the mean, we create an interval (mu+d, mu-d) with C% confidence. This
says that with C% probability, the *actual* mean lies in this interval.
We have to say this because there is a chance that the sample mean is 
not the actual mean ("population mean").  We build this confidence interval assuming
that the sample mean follows a normal distribution, and estimating *its* variance. All
this theory was covered in class.

How does this relate to your simulations? Say for a queueing system, you need to estimate
average response time. One simulation run, will give you one sample point of this average (after
discarding the transient, which is where Welch's procedure is used). So the mean
you got from one run is your X1. You will do n such independent runs, with different seeds,
and you will get average response time Xi, from each run i, giving you total n sample
points X1, X2, X3, ...Xn.  Now you must apply confidence interval theory to this sample.


Where's Welch's procedure in all this? Welch's procedure is simply to be used if you
are doing a simulation in which the *steady state* is of interest (this should be the
case for most of your simulations). If I am interested in *steady state average response time*, 
then using the values of say, the first few requests will not be representative. I should only 
use values after "warm up".  Welch's procedure simply gives a semi-rigourous (but quite heuristic) 
method to find the point after which the system can be assumed to have "warmed up". Thus, in the
delay example, suppose your simulation run i created m values of delay.  You should discard the
first value, and compute the average Xi based only on the last m-l values.  This "l" ca be determined
using Welch's procedure.